|
Fixed points and stability in neutral differential equations with variable delays
Author(s):
Chuhua
Jin;
Jiaowan
Luo
Journal:
Proc. Amer. Math. Soc.
136
(2008),
909-918.
MSC (2000):
Primary 34K20, 34K40
Posted:
November 30, 2007
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we consider a linear scalar neutral delay differential equation with variable delays and give some new conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved. The results of Burton, Raffoul, and Zhang are improved and generalized.
References:
-
- 1.
- T. A. Burton, Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, New York, 1985. MR 837654 (87f:34001)
- 2.
- T. A. Burton, Liapunov functionals, fixed points, and stability by Krasnoselskii's theorem, Nonlinear Studies, 9 (2001), 181-190. MR 1898587 (2003e:34133)
- 3.
- T. A. Burton, Stability by fixed point theory or Liapunov's theory: a comparison, Fixed Point Theory, 4 (2003), 15-32. MR 2031819 (2004j:34110)
- 4.
- T. A. Burton, Fixed points and stability of a nonconvolution equation, Proc. Amer. Math. Soc., 132 (2004), 3679-3687. MR 2084091 (2005g:34186)
- 5.
- T. A. Burton and T. Furumochi, A note on stability by Schauder's theorem, Funkcialaj Ekvacioj, 44 (2001), 73-82. MR 1847837 (2002d:34075)
- 6.
- T. A. Burton and T. Furumochi, Fixed points and problems in stability theory, Dynamical Systems and Appl., 10 (2001), 89-116. MR 1844329 (2002c:34076)
- 7.
- T. A. Burton and T. Furumochi, Krasnoselskii's fixed point theorem and stability, Nonlinear Analysis, 49 (2002), 445-454. MR 1886230 (2003e:34087)
- 8.
- Y. N. Raffoul, Stability in neutral nonlinear differential equations with functional delays using fixed-point theory, Mathematical and Computer Modelling, 40 (2004), 691-700. MR 2106161
- 9.
- B. Zhang, Fixed points and stability in differential equations with variable delays, Nonlinear Analysis, 63 (2005), e233-e242.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
34K20, 34K40
Retrieve articles in all Journals with MSC
(2000):
34K20, 34K40
Additional Information:
Chuhua
Jin
Affiliation:
Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou, Guangdong 510090, People's Republic of China
Email:
jinchuhua@tom.com
Jiaowan
Luo
Affiliation:
Corresponding author. School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, People's Republic of China
Email:
mathluo@yahoo.com
DOI:
10.1090/S0002-9939-07-09089-2
PII:
S 0002-9939(07)09089-2
Keywords:
Fixed points,
stability,
neutral delay differential equations,
variable delays.
Received by editor(s):
October 10, 2006
Posted:
November 30, 2007
Additional Notes:
The second author was supported in part by NNSF of China Grant \#10671043.
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org